Stochastic P-Bifurcation of Bistable van der Pol System under Fractional Gaussian Noise: Theory and Experiment

In this paper, the stochastic P-bifurcation problem of bistable van der Pol systems under fractional Gaussian noise (fGn) is discussed. Using the random average method to predict the stochastic dynamic behavior of the system under fGn and to obtain the stable probability density function of the response amplitude of the system, and then using the singularity theory to obtain the critical condition of stochastic P-bifurcation of the system. The results show that the H index in the fGn can induce the stochastic P-bifurcation in system, and the larger the H index is, the larger the stable probability density distribution becoming the bimodal region is. It indicates that the noise intensity required for the stochastic P-bifurcation becomes larger, which is beneficial to improve the stability of the equilibrium point of the system. At the same time, the system under the numerical simulation and circuit experiment has the same results as the theoretical analysis, which further insures the correctness of the research results.